Method of generating a result of a racing game

ABSTRACT

A method of generating a result of a racing game having a plurality of participants to enable fixed odds betting on the racing game. The result of the racing game is generated from the result of an identifier selection game. The method comprises allocating unique subsets of a set of identifiers used in the identifier selection game to each of the plurality of participants, defining a ranking of said participants from highest to lowest, running said identifier selection game by randomly selecting a result subset of identifiers from the set of identifiers, and determining first place in said race by determining which of said plurality of participants has the most identifiers of said result subset in the participant&#39;s allocated subset, and if two or more participants have the same number of identifiers in their respective allocated subsets, determining first place by determining which of the two or more participants is ranked highest.

FIELD OF THE PRESENT INVENTION

The present invention relates to a method and apparatus for generating aresult of a racing game which enables fixed odds betting on the game,the result of the racing game being generated from identifiers drawn inan identifier selection game.

BACKGROUND TO THE INVENTION

Keno is an ancient Chinese numbers game based on the drawing of 20 ballsfrom a cage containing 80 balls numbered 1,2, . . . , 80. In the lasttwenty or so years the game has become fully computerised and this haslead to a very fast game with a draw every 3-5 minutes. Manyjurisdictions allow the use of an internal software based resultgeneration technique using an approved pseudo Random Number Generator oran external “Black Box” result generator based on a softwarepseudo-Random Number Generator or a hardware white noise sampler.

Keno results are typically graphically presented as an 8×10 grid(matrix) as shown in FIG. 1.

Examples of common and exotic Keno bet types are as follows:

-   -   In the bet type “Spots & Ways”, players bet on N numbers        (1<=N<=15). The result is determined by finding out how many,        say C, of the N numbers were drawn (“caught”) and consulting a        Prize Table that specifies the prize for catching C from N;    -   In the bet type “Heads or Tails”, players bet on more numbers        being drawn from the lower 40 numbers—“Heads” OR vice        versa—“Tails” OR on an exact split (10:10) between the top &        bottom half—“Evens”. The result is determined by counting how        many of the drawn numbers are less than 41. If this exceeds 10        all “Heads” bettors win a published prize and all “Tails” &        “Evens” bettors lose. If this equals 10 all “Evens” bettors win        a different prize whilst all “Heads” & “Tails” bettors lose. If        it is less than 10 all “Tails” bettors win the same prize as the        “Head” prize whilst all “Evens” & “Tails” bettors lose.    -   In the bet type “Lucky Last”, players bet on the last number        drawn. A fixed prize is won if the selected number is the last        one drawn.    -   In the game “Keno Racing”, players bet on eight groups of ten        numbers (1 . . . 10), (11 . . . 20), . . . ,(71 . . . 80) The        groups are represented as a race between animated horses. As        each number is drawn, the horse whose group the number falls        within is moved forward a fixed amount. After the last number is        drawn and applied to “horse” movement, the most advanced “horse”        wins followed by next most advanced second & so on. Dead heats        are decided in favour of the first horse to arrive at the final        position—i.e. the first horse whose last number was drawn first.        A fixed prize, independent of the group number or “horse” is        offered for bets on the winner    -   In the game “Keno Roulette”, players bet on what part of the        matrix of FIG. 1 the first drawn number lies in. A variety of        pattern propositions are available to bet upon including:        -   “Straight Up”=nominate the exact first number;        -   “Quarters”=given the results matrix is divided into four            quarters, nominate which of the quarters the first number            resides within; and        -   “Rows”, “Corners”, etc.

Trackside is a game developed by the present applicant that provides ananimated race between a number of “participants”. Players are offeredfixed odds on a sub-set of standard horse racing bet types. The win oddsare nominated by the game operator and the system derives the place,quinella and trifecta odds from these using published algorithms. Eachgame result is generated by either an approved internal softwarealgorithm or an external mechanical ball draw taking into account theunequal chance of winning of each “participants”. For betting purposes,a Trackside result comprises the first three “participants”. These arecalled the race “placings”. After the winner has been determined from aset of 12 participants, second is determined by the same algorithm asused to determine the winner excepting the trial (“race”) is between 11participants and their respective chance of winning the trial for secondhas been adjusted to take account of removal of the winner of the trialfor first. Third placing is similarly determined by a further trialbetween the remaining 10 participants.

In a Win bet, players bet on which participant wins the race. Odds areoffered dependent on the participant number, for coming first past thepost (winning).

In a Place bet, players bet on a participant being placed. Odds areoffered dependent on the participant number, for being placed.

In an Each Way bet, players bet on a participant winning and/or beingplaced. Odds are offered dependent on the participant number, forwinning and/or being placed.

In a Quinella bet, players bet on two participants coming first andsecond in either order. Odds are offered based on each permutation ofthe quinella.

In a Trifecta bet, players bet on three contestants coming first, secondand third in exact nominated order. Odds are offered based on eachpermutation of the trifecta. Accordingly, it would be desirable togenerate a result for a Trackside type race game from a Keno typeidentifier draw game as this will allow Trackside type games to be runconcurrently with a Keno type game without the need to run a separaterandom number generator. Providing such a game may also provide anadditional enjoyable game to improve player enjoyment in conjunctionwith a Keno type game.

SUMMARY OF THE INVENTION

The invention provides a method of generating a result of a racing gamehaving a plurality of participants to enable fixed odds betting on theracing game, the result of the racing game being generated from theresult of an identifier selection game, the method comprising:

-   -   allocating unique subsets of a set of identifiers used in the        identifier selection game to each of the plurality of        participants;    -   defining a ranking of said participants from highest to lowest;    -   running said identifier selection game by randomly selecting a        result subset of identifiers from the set of identifiers; and    -   determining first place in said race by determining which of        said plurality of participants has the most identifiers of said        result subset in the participant's allocated subset, and if two        or more participants have the same number of identifiers in        their respective allocated subsets, determining first place by        determining which of the two or more participants is ranked        highest.

In embodiments where generating the result involves generating secondplace, and wherein if first place was determined by rank, second placeis determined by the next highest rank, and if first place is determinedby the number of identifiers in the allocated subset of the first placedparticipant, second place is determined as being the highest rankedparticipant which has the next greatest number of identifiers in theirallocated subset.

Further places can be allocated as necessary in an order defined firstlyby the number of identifiers in respective participant's allocatedsubsets and secondly by the relative rankings of the participants.

Thus, the results of the race are random but biased in accordance withthe ranking of participants thereby modifying the odds of participantswinning and allowing different odds to be offered on that basis.

Thus, if, as in one embodiment, the subsets are of equal size, thehighest ranked participant will have the lowest return on outlay, thesecond ranked participant will have the second lowest return on outlaywith the return on outlay increasing to a greatest return on the lowestranked participant.

In some embodiments of the invention, the spread of the odds can bevaried by allocating subsets of different numbers of identifiers to atleast some of the participants. Typically, this will involve allocatinglarger subsets to higher ranked participants than to lower rankedparticipants so that the relative odds of each participant winning areconsistent with the participant's ranking. However, this need notnecessarily be the case and larger subsets could be allocated in anotherway—for example, randomly—to obtain other interesting spreads of odds.

In one embodiment, the participants are horses in an animated horserace.

Typically, the identifiers will be numbers.

In one embodiment, the set of numbers is eighty numbers and the resultsubset consists of twenty numbers randomly selected from the set ofeighty.

The number of participants and the sizes of the subsets can be varied ina number of ways. For example: eight participants with subsets of ten;ten participants with subsets of eight; twelve participants with theeight highest ranked participants having subsets of seven and the fourlowest ranked participants having subsets of six; or twelve participantswith two participants having subsets of eight, six participants havingsubsets of seven, two participants having subsets of six and twoparticipants having subsets of five.

In one embodiment, the set of identifiers are displayed as a matrix andcontiguous portions of the matrix are allocated to each participant whenallocating the subsets, whereby it can readily be determined byinspecting the matrix to which participants identifiers in said resultset belong.

Apparatus for generating a result of a racing game having a plurality ofparticipants to enable fixed odds betting on the racing game the resultof the racing game being generated from the result of an identifierselection game, the apparatus comprising:

-   -   an identifier selector for randomly selecting a result subset of        identifiers from a set of identifiers to thereby generate a        result of the identifier selection game; and    -   a result generator for determining first place in said race by        determining which of said plurality of participants has the most        identifiers of said result subset in a participant allocated        unique subset of identifiers, and if two or more participants        have the same number of identifiers in their respective        allocated subsets, determining first place by determining which        of the two or more participants is ranked highest from        pre-allocated rankings of said participants from highest to        lowest.

In embodiments where generating the result involves generating a secondplace, if first place was determined by rank, the result generatordetermines second place by the next highest rank, where first place isdetermined by the number of identifiers in the allocated subset of thefirst placed participant, the result generator determines second placeas being the highest ranked participant which has the next greatestnumber of identifiers in their allocated subset.

The result generator can determine further places as necessary in anorder defined firstly by the number of identifiers and secondly by therelative rankings of the participants.

As in the method of the embodiments, the spread of the odds ofparticipants can be varied by pre-allocating subsets of differentnumbers of identifiers to respective participants.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a matrix of Keno results; and

FIG. 2 is a schematic diagram of an apparatus for determining the resultof a game.

DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 2 is a schematic diagram of an apparatus for determining the resultof an electronic game of the preferred embodiment. In the preferredembodiment, the electronic game is a horse racing game called Trackside™where players bet or wager on the result of the electronic game. Theindividual horses in the electronic game provide a plurality ofparticipants which can be bet upon. Players of the game can place fixedodds bets on the horses in the same manner as fixed odds bets can beplaced on conventional horse races. To stimulate customer interest insuch a game, it is necessary to allow players to bet at a variety ofhorses at different odds.

In the preferred embodiment, the electronic game is controlled bysoftware run by a computing device in the form of a processor of a hostcomputer 101. Once the result of the game has been determined, the hostcomputer 101 instructs the graphics engine 102 to create the horse racesimulation. The graphics engine 102 then causes the simulated horse raceto be displayed on displays 105.

To generate player interest in the game it is necessary to offer avariety of fixed odds bets with varying returns for player outlay sothat players can either seek to obtain a small return by betting on afavourite with a higher chance of winning or seek to obtain a largerreturn by betting on an outsider. The preferred embodiment provides atechnique for manipulating the results of identifier selection game suchas Keno where there are set of eighty numbers from which a subset oftwenty numbers are selected to generate the result of the racing game.It is preferred that the racing game is run in conjunction with the Kenogame so that when the result of the Keno game has been determined,simulation of the Trackside game occur in conjunction with display ofthe Keno result.

In the preferred embodiment, the method involves allocating uniquesubsets of a set of eighty numbers (identifiers) to each of theplurality of participants. A ranking is also allocated to theparticipants form highest to lowest. In the preferred embodiment, horseone has the highest ranking, horse two the second highest ranking etc.In a Keno draw, a set of twenty numbers referred to herein as theresults subset is drawn from the set of numbers. First place in the raceis determined by determining which of the horses has the most numbers ofthe result subset in their allocated subsets. If two or more horses havethe same number of identifiers in their respective allocated subsets,first place is determined by determining which of the two or more horsesis ranked higher.

The use of an arbitrary ranking in determination of the results biasesthe results so that the highest ranked horse will have a higher chanceof winning than the next highest ranked horse with the lowest rankedhorse having the lowest chance of winning. Accordingly, as the chancesof individual horses vary unlike in conventional Keno Racing, differentodds can be offered on different horses.

Subsequent places are also allocated in an order defined firstly by thenumber of identifiers of a horse's subset which are in the result subsetand secondly by the relative rankings of the participants. Thus, thebias towards higher ranked horses will be continued in the allocation offurther places.

In a typical Trackside game, the result is determined by determining theidentity of the first three place getters. This result is then animatedand displayed as described above. Players can bet on the chance of anindividual horse winning or the chance of a horse obtaining a place.Players can also bet using other conventional horse racing bet typessuch as:

-   -   quinellas where the player bets on the first and second place        getters in a race;    -   an exacta where the bet is placed on the first and second places        but where order is important; and    -   on a trifecta where bets are placed on the first three place        getters.

When the preferred embodiment is run in conjunction with a Keno draw,the subsets of numbers which are allocated to individual horses arepreferably chosen so that they are next to one another (i.e. contiguous)in the matrix of Keno results which is normally displayed as an eight byten grid or two four by ten grids as shown in FIG. 1. In a typical Kenogame, the results are displayed by highlighting individual numbers onthe grid of eighty numbers to show that they belong to the result subsetas shown in FIG. 1 by the bold numbers. By choosing subsets of numbersfor each horse which are next to one another, a person watching the Kenoresult can readily see in which part of the matrix the resultidentifiers are falling and thereby monitor the chances of a horse theyhave bet on winning. Typically, a Keno draw involves an animation of theresults which have previously been chosen using a standard techniquesuch as random number generation. If, as in one embodiment, this isdisplayed alongside an animated horse race the player can see forexample on one display screen the Keno results as they are drawn and onthe other display screen the animated horse race and so will beencouraged if they see that two or three numbers have been drawn earlyin the Keno draw in the subset which belongs to the horse they haveselected, thus building excitement in the game.

Several examples of possible numbers of horses and subset sizes will nowbe described to further illustrate the preferred embodiment.

EXAMPLE 1

In the first example there are a field of eight runners in the gameranked from highest (horse 1) to lowest (horse 8). Each participant(runner) is represented by ten Keno balls in the matrix as shown in FIG.3 where each horse has a row of Keno numbers. With eighty Keno balls inthe Keno matrix and twenty drawn Keno balls relevant to determine raceresult there are 796,510 different outcomes of ball quantities drawnagainst each runner.

In this example, each runner has the same quantity of Keno balls butwhen two runners have the same quantity of balls drawn, the lowernumbered runner (i.e. higher ranked) ranks above a higher numberedrunner. The order of the balls drawn from Keno is not relevant to derivethe result.

The win, place, and quinella dividends are shown in Tables 1, 2 and 3respectively including the return to player (RTP). TABLE 1 WIN DIVIDENDSCALCULATOR Target Desired RTP 80% Actual Dividend Rounded $1 RoundedPlayer Result Probability for $1 Dividend Return 1 19.5292% $4.10 $4.1080.0697% 2 16.4032% $4.88 $4.90 80.3756% 3 14.1236% $5.66 $5.70 80.5047%4 12.3941% $6.45 $6.50 80.5618% 5 11.0092% $7.27 $7.30 80.3668% 69.8381% $8.13 $8.10 79.6887% 7 8.8092% $9.08 $9.10 80.1638% 8 7.8934%$10.14 $10.10 79.7233% TOTAL 100.0000% AVERAGE: 80.1818%

TABLE 2 PLACE DIVIDENDS CALCULATOR Target Desired RTP 80% ActualDividend Rounded $1 Rounded Player Result Probability for $1 DividendReturn 1 48.9347% $1.63 $1.60 78.2954% 2 46.3314% $1.73 $1.70 78.7634% 343.4129% $1.84 $1.80 78.1432% 4 39.9514% $2.00 $2.00 79.9027% 5 36.0390%$2.22 $2.20 79.2859% 6 31.9875% $2.50 $2.50 79.9688% 7 28.2158% $2.84$2.80 79.0042% 8 25.1274% $3.18 $3.20 80.4076% TOTAL 300.0000%  AVERAGE:79.2214%

TABLE 3 QUINELLA DIVIDENDS CALCULATOR Target Desired RTP 80% ActualDividend Rounded $1 Rounded Player Result Probability for $1 DividendReturn 1 & 2 8.0990% $9.88 $9.90 80.1803% 1 & 3 6.5235% $12.26 $12.3080.2386% 1 & 4 5.4496% $14.68 $14.70 80.1086% 1 & 5 4.7437% $16.86$16.90 80.1688% 1 & 6 4.2943% $18.63 $18.60 79.8740% 1 & 7 4.0092%$19.95 $20.00 80.1840% 1 & 8 3.8155% $20.97 $21.00 80.1256% 2 & 35.7943% $13.81 $13.80 79.9619% 2 & 4 4.7204% $16.95 $16.90 79.7756% 2 &5 4.0146% $19.93 $19.90 79.8905% 2 & 6 3.5652% $22.44 $22.40 79.8600% 2& 7 3.2801% $24.39 $24.40 80.0339% 2 & 8 3.0864% $25.92 $25.90 79.9374%3 & 4 4.1966% $19.06 $19.10 80.1549% 3 & 5 3.4907% $22.92 $22.9079.9380% 3 & 6 3.0413% $26.30 $26.30 79.9869% 3 & 7 2.7562% $29.03$29.00 79.9305% 3 & 8 2.5625% $31.22 $31.20 79.9510% 4 & 5 3.1294%$25.56 $25.60 80.1138% 4 & 6 2.6800% $29.85 $29.90 80.1329% 4 & 72.3949% $33.40 $33.40 79.9906% 4 & 8 2.2012% $36.34 $36.30 79.9048% 5 &6 2.4445% $32.73 $32.70 79.9365% 5 & 7 2.1594% $37.05 $37.00 79.8993% 5& 8 1.9657% $40.70 $40.70 80.0059% 6 & 7 2.0165% $39.67 $39.70 80.0537%6 & 8 1.8228% $43.89 $43.90 80.0198% 7 & 8 1.7422% $45.92 $45.9079.9658% TOTAL 100.0000%  AVERAGE: 80.0116%

EXAMPLE 2

In the second example, there is a field of ten runners in the game withhorse 1 being the highest ranked and horse 10 being the lowest ranked.Each runner is represented by eight Keno balls in the matrix as shown inFIG. 4 where each horse has a column. With eighty Keno balls in the Kenomatrix and twenty drawn Keno results relevant to determine race resultthere are 8,337,880 different outcomes of ball quantities drawn againsteach runner.

The win, place and quinella dividends are shown in Tables 4, 5 and 6respectively. It will be apparent that the use of ten runners gives abroader spread of odds than the field of eight runners of Example 1.TABLE 4 WIN DIVIDENDS CALCULATOR Target Desired RTP 80% Actual DividendRounded $1 Rounded Player Result Probability for $1 Dividend Return 117.6013% $4.55 $4.50 79.2060% 2 14.8092% $5.40 $5.40 79.9699% 3 12.5798%$6.36 $6.40 80.5108% 4 10.8112% $7.40 $7.40 80.0027% 5 9.4199% $8.49$8.50 80.0693% 6 8.3323% $9.60 $9.60 79.9899% 7 7.4837% $10.69 $10.7080.0754% 8 6.8183% $11.73 $11.70 79.7744% 9 6.2888% $12.72 $12.7079.8674% 10 5.8555% $13.66 $13.70 80.2199% TOTAL 100.0000% 1 AVERAGE:79.9686%

TABLE 5 PLACE DIVIDENDS CALCULATOR Target Desired RTP 80% ActualDividend Rounded $1 Rounded Player Result Probability for $1 DividendReturn 1 42.3764% $1.89 $1.90 80.5152% 2 37.7288% $2.12 $2.10 79.2306% 334.2584% $2.34 $2.30 78.7943% 4 31.8338% $2.51 $2.50 79.5844% 5 30.0370%$2.66 $2.70 81.0999% 6 28.4407% $2.81 $2.80 79.6339% 7 26.7758% $2.99$3.00 80.3274% 8 24.9304% $3.21 $3.20 79.7773% 9 22.8964% $3.49 $3.5080.1376% 10 20.7223% $3.86 $3.90 80.8169% TOTAL 300.0000%  1 AVERAGE:79.9917%

TABLE 6 QUINELLA DIVIDENDS CALCULATOR Target Desired RTP 80% ActualDividend Rounded $1 Rounded Player Result Probability for $1 DividendReturn 1 & 2 5.6049% $14.27 $14.30 80.1501% 1 & 3 4.7232% $16.94 $16.9079.8214% 1 & 4 4.0454% $19.78 $19.80 80.0987% 1 & 5 3.4979% $22.87$22.90 80.1024% 1 & 6 3.0524% $26.21 $26.20 79.9720% 1 & 7 2.6940%$29.70 $29.70 80.0118% 1 & 8 2.4116% $33.17 $33.20 80.0659% 1 & 92.1950% $36.45 $36.40 79.8994%  1 & 10 2.0346% $39.32 $39.30 79.9588% 2& 3 4.4041% $18.16 $18.20 80.1542% 2 & 4 3.7263% $21.47 $21.50 80.1156%2 & 5 3.1788% $25.17 $25.20 80.1067% 2 & 6 2.7333% $29.27 $29.3080.0851% 2 & 7 2.3749% $33.69 $33.70 80.0346% 2 & 8 2.0925% $38.23$38.20 79.9350% 2 & 9 1.8760% $42.64 $42.60 79.9156%  2 & 10 1.7155%$46.63 $46.60 79.9419% 3 & 4 3.5093% $22.80 $22.80 80.0128% 3 & 52.9619% $27.01 $27.00 79.9704% 3 & 6 2.5163% $31.79 $31.80 80.0187% 3 &7 2.1579% $37.07 $37.10 80.0597% 3 & 8 1.8756% $42.65 $42.70 80.0868% 3& 9 1.6590% $48.22 $48.20 79.9630%  3 & 10 1.4985% $53.39 $53.4080.0210% 4 & 5 2.7918% $28.66 $28.70 80.1241% 4 & 6 2.3462% $34.10$34.10 80.0063% 4 & 7 1.9879% $40.24 $40.20 79.9119% 4 & 8 1.7055%$46.91 $46.90 79.9872% 4 & 9 1.4889% $53.73 $53.70 79.9538%  4 & 101.3284% $60.22 $60.20 79.9718% 5 & 6 2.2043% $36.29 $36.30 80.0154% 5 &7 1.8459% $43.34 $43.30 79.9281% 5 & 8 1.5635% $51.17 $51.20 80.0532% 5& 9 1.3470% $59.39 $59.40 80.0091%  5 & 10 1.1865% $67.43 $67.4079.9695% 6 & 7 1.7266% $46.33 $46.30 79.9412% 6 & 8 1.4442% $55.39$55.40 80.0096% 6 & 9 1.2276% $65.17 $65.20 80.0415%  6 & 10 1.0672%$74.96 $75.00 80.0376% 7 & 8 1.3451% $59.48 $59.50 80.0328% 7 & 91.1285% $70.89 $70.90 80.0109%  7 & 10 0.9680% $82.64 $82.60 79.9602% 8& 9 1.0477% $76.36 $76.40 80.0452%  8 & 10 0.8872% $90.17 $90.2080.0299%  9 & 10 0.8230% $97.20 $97.20 79.9991% TOTAL 100.0000%  1AVERAGE: 80.0120%

EXAMPLE 3

In the third example there is a field of twelve runners in the game.Each runner is represented by 6 or 7 Keno balls in the matrix as shownin FIG. 5. The top eight ranked horses (numbers 1-8) are allocatedsubsets of seven numbers and the other horses (9-12) are allocated sixnumbers. For eighty Keno balls in the Keno matrix and twenty drawn Kenoresults relevant to determine race result, there are 64,123,367different outcomes of ball quantities drawn against each runner. Again,when two runners have the same quantity of balls drawn, the lowernumbered runner ranks above a higher numbered runner.

As shown in Tables 7, 8 and 9, this provides a still greater spread ofodds for wins, places, quinellas and trifectas than in the previousexamples. Indeed, the least likely trifecta in this Example will producea payout of about $600,000 unless a cap (e.g. $100,000) is applied tothe trifecta as may be appropriated. This is significantly larger thanthe largest trifecta for example 2 which is in the order of $16,000 foran 80% return to player. TABLE 7 WIN DIVIDENDS CALCULATOR Target DesiredRTP 80% Actual Dividend Rounded $1 Rounded Player Result Probability for$1 Dividend Return 1 17.2259% $4.64 $4.60 79.2391% 2 14.6928% $5.44$5.40 79.3412% 3 12.6835% $6.31 $6.30 79.9059% 4 11.0248% $7.26 $7.3080.4810% 5 9.6308% $8.31 $8.30 79.9356% 6 8.4554% $9.46 $9.50 80.3263% 77.4686% $10.71 $10.70 79.9138% 8 6.6461% $12.04 $12.00 79.7531% 93.4239% $23.37 $23.40 80.1188% 10 3.1442% $25.44 $25.40 79.8622% 112.9042% $27.55 $27.50 79.8643% 12 2.6999% $29.63 $29.60 79.9178% TOTAL100.0000% 1 AVERAGE: 79.8883%

TABLE 8 PLACE DIVIDENDS CALCULATOR Target Desired RTP 80% ActualDividend Rounded $1 Rounded Player Result Probability for $1 DividendReturn 1 44.3587% $1.80 $1.80 79.8456% 2 39.3150% $2.03 $2.00 78.6299% 334.3753% $2.33 $2.30 79.0633% 4 30.1470% $2.65 $2.70 81.3970% 5 26.9330%$2.97 $3.00 80.7990% 6 24.6958% $3.24 $3.20 79.0264% 7 23.1853% $3.45$3.50 81.1486% 8 22.0941% $3.62 $3.60 79.5387% 9 14.4502% $5.54 $5.5079.4759% 10 13.9697% $5.73 $5.70 79.6271% 11 13.4912% $5.93 $5.9079.5978% 12 12.9849% $6.16 $6.20 80.5062% TOTAL 300.0000%  1 AVERAGE:79.8880%

TABLE 9 QUINELLA DIVIDENDS CALCULATOR Target Desired RTP 80% ActualDividend Rounded $1 Rounded Player Result Probability for $1 DividendReturn 1 & 2 5.1511% $15.53 $15.50 79.8426% 1 & 3 4.2043% $19.03 $19.0079.8817% 1 & 4 3.6177% $22.11 $22.10 79.9516% 1 & 5 3.2163% $24.87$24.90 80.0854% 1 & 6 2.9101% $27.49 $27.50 80.0279% 1 & 7 2.6572%$30.11 $30.10 79.9809% 1 & 8 2.4397% $32.79 $32.80 80.0237% 1 & 91.4018% $57.07 $57.10 80.0406%  1 & 10 1.3176% $60.72 $60.70 79.9793%  1& 11 1.2409% $64.47 $64.50 80.0388%  1 & 12 1.1713% $68.30 $68.3080.0009% 2 & 3 3.7812% $21.16 $21.20 80.1616% 2 & 4 3.1946% $25.04$25.00 79.8657% 2 & 5 2.7932% $28.64 $28.60 79.8853% 2 & 6 2.4870%$32.17 $32.20 80.0818% 2 & 7 2.2341% $35.81 $35.80 79.9801% 2 & 82.0167% $39.67 $39.70 80.0612% 2 & 9 1.1433% $69.98 $70.00 80.0283%  2 &10 1.0591% $75.53 $75.50 79.9631%  2 & 11 0.9824% $81.43 $81.40 79.9682% 2 & 12 0.9128% $87.64 $87.60 79.9626% 3 & 4 2.9587% $27.04 $27.0079.8851% 3 & 5 2.5573% $31.28 $31.30 80.0426% 3 & 6 2.2511% $35.54$35.50 79.9139% 3 & 7 1.9982% $40.04 $40.00 79.9265% 3 & 8 1.7807%$44.93 $44.90 79.9551% 3 & 9 1.0038% $79.69 $79.70 80.0065%  3 & 100.9197% $86.99 $87.00 80.0138%  3 & 11 0.8430% $94.90 $94.90 80.0002%  3& 12 0.7734% $103.44 $103.40 79.9696% 4 & 5 2.4205% $33.05 $33.1080.1190% 4 & 6 2.1143% $37.84 $37.80 79.9218% 4 & 7 1.8614% $42.98$43.00 80.0402% 4 & 8 1.6440% $48.66 $48.70 80.0616% 4 & 9 0.9270%$86.30 $86.30 79.9985%  4 & 10 0.8428% $94.92 $94.90 79.9850%  4 & 110.7661% $104.42 $104.40 79.9841%  4 & 12 0.6965% $114.85 $114.9080.0320% 5 & 6 2.0268% $39.47 $39.50 80.0569% 5 & 7 1.7738% $45.10$45.10 79.9994% 5 & 8 1.5564% $51.40 $51.40 79.9988% 5 & 9 0.8805%$90.85 $90.90 80.0407%  5 & 10 0.7964% $100.45 $100.50 80.0371%  5 & 110.7197% $111.16 $111.20 80.0290%  5 & 12 0.6501% $123.06 $123.1080.0261% 6 & 7 1.7095% $46.80 $46.80 80.0032% 6 & 8 1.4920% $53.62$53.60 79.9737% 6 & 9 0.8479% $94.36 $94.40 80.0378%  6 & 10 0.7637%$104.75 $104.80 80.0369%  6 & 11 0.6870% $116.45 $116.40 79.9676%  6 &12 0.6174% $129.57 $129.60 80.0166% 7 & 8 1.4390% $55.60 $55.60 80.0057%7 & 9 0.8213% $97.40 $97.40 79.9995%  7 & 10 0.7372% $108.52 $108.5079.9865%  7 & 11 0.6605% $121.12 $121.10 79.9864%  7 & 12 0.5909%$135.39 $135.40 80.0084% 8 & 9 0.7981% $100.24 $100.20 79.9711%  8 & 100.7140% $112.05 $112.00 79.9644%  8 & 11 0.6373% $125.54 $125.5079.9767%  8 & 12 0.5677% $140.93 $140.90 79.9846%  9 & 10 0.4393%$182.10 $182.10 79.9991%  9 & 11 0.3904% $204.91 $204.90 79.9956%  9 &12 0.3460% $231.21 $231.20 79.9951% 10 & 11 0.3812% $209.87 $209.9080.0109% 10 & 12 0.3368% $237.55 $237.50 79.9835% 11 & 12 0.3282%$243.79 $243.80 80.0046% TOTAL 100.0000% 1 AVERAGE: 79.9964%

EXAMPLE 4

In the fourth example there is a field of 12 runners in the game. Eachrunner is represented by 5, 6, 7 or 8 Keno balls in the matrix as shownin FIG. 6. Horses 1 and 2 are allocated eight numbers, horses 3 to 8 areallocated seven numbers, horses 9 and 10 are allocated six numbers andhorses 11 and 12 are allocated five numbers.

For eighty Keno balls in the Keno matrix and twenty drawn Keno resultsrelevant to determine race result, there are 61,705,898 differentoutcomes of ball quantities drawn against each runner.

The win, place and quinella odds are shown in Tables 10, 11 and 12respectively. TABLE 10 WIN DIVIDENDS CALCULATOR Target Desired RTP 80%Actual Dividend Rounded $1 Rounded Player Result Probability for $1Dividend Return 1 23.1121% $3.46 $3.50 80.8924% 2 19.1499% $4.18 $4.2080.4295% 3 11.1559% $7.17 $7.20 80.3223% 4 9.7239% $8.23 $8.20 79.7361%5 8.5227% $9.39 $9.40 80.1136% 6 7.5145% $10.65 $10.60 79.6537% 76.6727% $11.99 $12.00 80.0726% 8 5.9751% $13.39 $13.40 80.0658% 93.0472% $26.25 $26.30 80.1411% 10 2.8148% $28.42 $28.40 79.9416% 111.1896% $67.25 $67.20 79.9440% 12 1.1216% $71.33 $71.30 79.9666% TOTAL100.0000% 1 AVERAGE: 80.1066%

TABLE 11 PLACE DIVIDENDS CALCULATOR Target Desired RTP 80% ActualDividend Rounded $1 Rounded Player Result Probability for $1 DividendReturn 1 52.1702% $1.53 $1.50 78.2553% 2 47.0155% $1.70 $1.70 79.9263% 333.7143% $2.37 $2.40 80.9143% 4 29.5209% $2.71 $2.70 79.7063% 5 26.3864%$3.03 $3.00 79.1592% 6 24.2040% $3.31 $3.30 79.8733% 7 22.6916% $3.53$3.50 79.4205% 8 21.5454% $3.71 $3.70 79.7180% 9 14.0000% $5.71 $5.7079.7998% 10 13.4737% $5.94 $5.90 79.4946% 11  7.7413% $10.33 $10.3079.7355% 12  7.5368% $10.61 $10.60 79.8903% TOTAL 300.0000%  AVERAGE:79.6578%

TABLE 12 QUINELLA DIVIDENDS CALCULATOR Target Desired RTP 80% ActualDividend Rounded $1 Rounded Player Result Probability for $1 DividendReturn 1 & 2 8.8357% $9.05 $9.10 80.4052% 1 & 3 5.1655% $15.49 $15.5080.0657% 1 & 4 4.4528% $17.97 $18.00 80.1506% 1 & 5 3.9471% $20.27$20.30 80.1253% 1 & 6 3.5529% $22.52 $22.50 79.9399% 1 & 7 3.2253%$24.80 $24.80 79.9879% 1 & 8 2.9447% $27.17 $27.20 80.0965% 1 & 91.6688% $47.94 $47.90 79.9342%  1 & 10 1.5609% $51.25 $51.30 80.0759%  1& 11 0.7837% $102.08 $102.10 80.0160%  1 & 12 0.7481% $106.94 $106.9079.9676% 2 & 3 4.6588% $17.17 $17.20 80.1306% 2 & 4 3.9460% $20.27$20.30 80.1045% 2 & 5 3.4403% $23.25 $23.30 80.1586% 2 & 6 3.0461%$26.26 $26.30 80.1127% 2 & 7 2.7185% $29.43 $29.40 79.9252% 2 & 82.4379% $32.81 $32.80 79.9647% 2 & 9 1.3660% $58.57 $58.60 80.0472%  2 &10 1.2582% $63.59 $63.60 80.0186%  2 & 11 0.6226% $128.50 $128.5080.0004%  2 & 12 0.5869% $136.30 $136.30 79.9985% 3 & 4 2.5429% $31.46$31.50 80.1012% 3 & 5 2.2015% $36.34 $36.30 79.9140% 3 & 6 1.9344%$41.36 $41.40 80.0859% 3 & 7 1.7114% $46.75 $46.70 79.9216% 3 & 81.5196% $52.65 $52.60 79.9313% 3 & 9 0.8497% $94.15 $94.10 79.9586%  3 &10 0.7757% $103.13 $103.10 79.9734%  3 & 11 0.3831% $208.83 $208.8079.9896%  3 & 12 0.3586% $223.11 $223.10 79.9966% 4 & 5 2.0908% $38.26$38.30 80.0792% 4 & 6 1.8238% $43.86 $43.90 80.0645% 4 & 7 1.6007%$49.98 $50.00 80.0367% 4 & 8 1.4090% $56.78 $56.80 80.0288% 4 & 90.7886% $101.45 $101.40 79.9641%  4 & 10 0.7146% $111.96 $112.0080.0318%  4 & 11 0.3538% $226.09 $226.10 80.0022%  4 & 12 0.3293%$242.93 $242.90 79.9898% 5 & 6 1.7497% $45.72 $45.70 79.9620% 5 & 71.5267% $52.40 $52.40 79.9968% 5 & 8 1.3349% $59.93 $59.90 79.9593% 5 &9 0.7498% $106.69 $106.70 80.0082%  5 & 10 0.6758% $118.38 $118.4080.0161%  5 & 11 0.3370% $237.42 $237.40 79.9935%  5 & 12 0.3124%$256.05 $256.10 80.0141% 6 & 7 1.4700% $54.42 $54.40 79.9704% 6 & 81.2783% $62.58 $62.60 80.0195% 6 & 9 0.7212% $110.92 $110.90 79.9842%  6& 10 0.6472% $123.61 $123.60 79.9935%  6 & 11 0.3254% $245.86 $245.9080.0124%  6 & 12 0.3009% $265.90 $265.90 79.9993% 7 & 8 1.2306% $65.01$65.00 79.9902% 7 & 9 0.6974% $114.71 $114.70 79.9919%  7 & 10 0.6234%$128.33 $128.30 79.9784%  7 & 11 0.3160% $253.13 $253.10 79.9903%  7 &12 0.2915% $274.43 $274.40 79.9927% 8 & 9 0.6764% $118.27 $118.3080.0187%  8 & 10 0.6024% $132.81 $132.80 79.9952%  8 & 11 0.3078%$259.88 $259.90 80.0057%  8 & 12 0.2833% $282.38 $282.40 80.0065%  9 &10 0.3685% $217.11 $217.10 79.9963%  9 & 11 0.1904% $420.10 $420.1080.0004%  9 & 12 0.1748% $457.75 $457.80 80.0087% 10 & 11 0.1872%$427.44 $427.40 79.9922% 10 & 12 0.1715% $466.48 $466.50 80.0029% 11 &12 0.0951% $840.89 $840.90 80.0013% TOTAL 100.0000%  AVERAGE: 80.0181%

It will apparent to persons skilled in the art that any otherappropriate arrangement of number of participants and size of subsetscan be chosen in order to vary the spread of the odds. Considerationswill include providing an appropriate spread of odds from highest tolowest ranked horse. Typically where subsets of different sizes areallocated, this will be done by allocating bigger subsets of identifiersto the higher ranked horses and lower numbers to lower ranked horses tothereby spread the odds. However, persons skilled in the art willappreciate that other permutations may be desirable in order to vary theodds. For example, if it is desired to have one or two horses in therace which have more similar odds than are otherwise available becauseof the pre-eminence given to the highest ranked horse.

Persons skilled in the art will also appreciate that the highest rankedhorse need not be numbered horse number one and that other horsenumberings could be used or indeed names could be used in order toidentify horses. Thus it will be appreciated that herein the term “rank”is used to indicate the order in which horses are favoured indetermining the result. These and other variations will be apparent topersons skilled in the art. For example, the racing game could be runusing ball draw out of different numbers of balls so that it can be runin conjunction with other number draw games or, run independently of aball selection game. The number of identifiers in the set of identifiersand the number of identifiers in the result subset can be varied inorder to vary the odds of the game and the participants are horses.

Persons skilled in the art will also appreciate that the method of thepreferred embodiment can readily be encoded in software to run on thehost computer 101. In this respect, the host computer 101 may includethe identifier selector which selects a random subset of identifiersfrom a set of identifiers or the identifier selector may be provided byan alternative piece of apparatus. For example, a computer configured togenerate a Keno result to thereby keep the two processes separate.

Further modifications will be apparent to persons skilled in the art andfall within the scope of this invention.

1. A method of generating a result of a racing game having a pluralityof participants to enable fixed odds betting on the racing game, theresult of the racing game being generated from the result of anidentifier selection game, the method comprising: allocating uniquesubsets of a set of identifiers used in the identifier selection game toeach of the plurality of participants; defining a ranking of saidparticipants from highest to lowest; running said identifier selectiongame by randomly selecting a result subset of identifiers from the setof identifiers; and determining first place in said race by determiningwhich of said plurality of participants has the most identifiers of saidresult subset in the participant's allocated subset, and if two or moreparticipants have the same number of identifiers in their respectiveallocated subsets, determining first place by determining which of thetwo or more participants is ranked highest.
 2. A method as claimed inclaim 1, wherein generating the result involves generating second place,and wherein if first place was determined by rank, second place isdetermined by the next highest rank, and if first place is determined bythe number of identifiers in the allocated subset of the first placedparticipant, second place is determined as being the highest rankedparticipant which has the next greatest number of identifiers of theirallocated subset.
 3. A method as claimed in claim 2, wherein furtherplaces are decided as necessary in an order defined firstly by thenumber of identifiers in respective participant's allocated subsets andsecondly by the relative rankings of the participants.
 4. A method asclaimed in claim 1 wherein each participant's subset is the same size.5. A method as claimed in claim 1 comprising allocating subsets ofdifferent numbers of identifiers to at least some of the participants.6. A method as claimed in claim 5 comprising allocating larger subsetsto higher ranked participants than to lower ranked participants so thatthe relative odds of each participant winning are consistent with theparticipant's ranking.
 7. A method as claimed in claim 1 wherein theparticipants are horses in an animated horse race.
 8. A method asclaimed in claim 1 wherein identifiers are numbers.
 9. A method asclaimed in claim 8 wherein the set of numbers is eighty numbers and theresult subset consists of twenty numbers randomly selected from the setof eighty.
 10. A method as claimed in claim 1 wherein the number ofparticipants and the sizes of the subsets is selected from one of: eightparticipants with a subset size of ten; ten participants with subsets ofeight; twelve participants with the eight highest ranked participantshaving subsets of seven and the four lowest ranked participants havingsubsets of six; twelve participants with two participants having subsetsof eight, six participants having subsets of seven, two participantshaving subsets of six and two participants having subsets of five.
 11. Amethod as claimed in claim 1, wherein the set of identifiers aredisplayed as a matrix and contiguous portions of the matrix areallocated to each participant when allocating the subsets, whereby itcan readily be determined by inspecting the matrix to which participantidentifiers in said result set belong.
 12. Apparatus for generating aresult of a racing game having a plurality of participants to enablefixed odds betting on the racing game the result of the racing gamebeing generated from the result of an identifier selection game, theapparatus comprising: an identifier selector for randomly selecting aresult subset of identifiers from a set of identifiers to therebygenerate a result of the identifier selection game; and a resultgenerator for determining first place in said race by determining whichof said plurality of participants has the most identifiers of saidresult subset in a participant allocated unique subsets of identifiers,and if two or more participants have the same number of identifiers intheir respective allocated subsets, determining first place bydetermining which of the two or more participants is ranked highest frompre-allocated rankings of said participants from highest to lowest. 13.Apparatus as claimed in claim 12 wherein generating the result involvesgenerating a second place, and wherein the result generator isconfigured such that if first place was determined by rank, the resultgenerator determines second place by the next highest rank, if firstplace is determined by the number of identifiers in the allocated subsetof the first placed participant, the result generator determines secondplace as being the highest ranked participant which has the nextgreatest number of identifiers in their allocated subset.
 14. Apparatusas claimed in claim 13 wherein the result generator is configured todetermine further places as necessary in an order defined firstly by thenumber of identifiers and secondly by the relative rankings of theparticipants.
 15. Apparatus as claimed in claim 12 wherein saididentifier selector comprises a computing device that constitutes saididentifier selector and said result generator, said computing devicehaving a memory for storing said allocated identifiers and saidrankings.